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Mathematics informs optogenetic stimulation of brain tissue

Optogenetic techniques allow neurophysiologists to directly stimulate neurons with light. It is often assumed that the dynamical behaviour of the neural tissue is unchanged. However recent observations of optogenetically-induced travelling waves provide a clue that this may not be the case. Lu et al (2015) found that constant stimulation of macaque cortex elicited 40-80 Hz oscillations in the local field potential in a manner consistent with Type II neural excitability. Furthermore, those oscillations propagated far into the surrounding cortical tissue well beyond the reach of the stimulation.

Mathematical theory suggests that only neural tissue with Type I excitability can sustain propagating waves. So how can cortical tissue simultaneously exhibit both Type I and Type II excitability? We investigated the apparent contradiction by modelling the cortex as recurrently-connected excitatory and inhibitory neurons. Such models exhibit either Type I or Type II excitability depending upon the choice of parameters. We found that optogenetic stimulation can locally transform Type I excitability into Type II excitability by preferentially targeting inhibitory cells. The findings shed new light on how optogenetic stimulation can alter the response dynamics of neural tissue.

Space-time plots of the cortical model in one spatial dimension. Optogenetic stimulation was applied focally at position x=0. Panels A-C show cases of weak, medium, and strong stimulation respectively. 40-80 Hz oscillations arose gradually from the stimulation site via Type II excitability. Waves were emitted from the stimulation site via Type I excitability once the simulation reached a critical threshold. The simulated medium thus exhibited co-existing Type I and Type II excitability in agreement with neurophysiological observations.